Verified Solution • 2025–26 Session moderate

QJEEM22Ma981f: JEE Main 2022 Mathematics - Class 12 JEEM22Ma981f Solution: A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its…

A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is 1n{1 \over n} . If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48, is :

Multiple Choice Options

  • A 7211{7 \over {{2^{11}}}}
  • B 7212{7 \over {{2^{12}}}}
  • C 3210{3 \over {{2^{10}}}}
  • D 13212{{13} \over {{2^{12}}}}

Step-by-Step Verified Solution

There are only two ways to get sum 48, which are (32, 8, 8) and (16, 16, 16)

So, required probability

=3(232 . 18 . 18)+(116 . 116 . 116)= 3\left( {{2 \over {32}}\,.\,{1 \over 8}\,.\,{1 \over 8}} \right) + \left( {{1 \over {16}}\,.\,{1 \over {16}}\,.\,{1 \over {16}}} \right)

=3210+1212= {3 \over {{2^{10}}}} + {1 \over {{2^{12}}}}

=13212= {{13} \over {{2^{12}}}}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring